right triangleXYZ with hypotenuse line segment YZ, the length of line segment XY is b units long, and the length of line segment XZ is three times the length of line segment XY
The length of the hypotenuse side of the right triangle ΔXYZ, found using Pythagorean Theorem is b·√(10)
What is Pythagorean Theorem?Pythagorean Theorem indicates that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the square of the legs of the right triangle.
The specified parameters of triangle are;
The hypotenuse of the triangle, ΔXYZ = [tex]\overline{YZ}[/tex]
The length of the legs of the right triangle are;
[tex]\overline{XY}[/tex] = b, and [tex]\overline{XZ}[/tex] = 3 × [tex]\overline{XY}[/tex]
Therefore;
[tex]\overline{XZ}[/tex] = 3 × b (substitution property of equality)
The length of the hypotenuse side can be calculated as follows;
Therefore;, according to Pythagorean theorem, we get;
[tex]\overline{YZ}[/tex]² = [tex]\overline{XY}[/tex]² + [tex]\overline{XY}[/tex]²
[tex]\overline{YZ}[/tex]² = b² + (3·b)² = b² + 9·b² = 10·b²
[tex]\overline{YZ}[/tex] = [tex]\sqrt{10\cdot b^2} = b \cdot \sqrt{10}[/tex]
The length of the hypotenuse side , [tex]\overline{YZ}[/tex] = b·√(10)
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verify that (sin x -cos x)^2 =1-2 sin x cos x is an identity
By trigonometric formulas and algebra properties, the equivalence between the trigonometric expression (sin x - cos x)² and the trigonometric expression 1 - 2 · sin x · cos x.
How to prove the equivalence between two trigonometric expressions
In this problem we need to prove if the trigonometric expression (sin x - cos x)² is equivalent to the trigonometric expression 1 - 2 · sin x · cos x, this can be proved by trigonometric formulas and algebra properties. First, write the initial expression:
(sin x - cos x)²
Second, expand the binomial:
sin² x - 2 · sin x · cos x + cos² x
Third, use the fundamental trigonometric expression:
1 - 2 · sin x · cos x
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NO LINKS!! Each table below represents an exponential function of the form y = ab^x. Complete each table and find the corresponding equation.
Answer:
[tex]\textsf{a)} \quad y=1.8(3.2)^x[/tex]
[tex]\textsf{b)} \quad y=5(7)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (a)Given ordered pairs:
(0, 1.8)(1, 5.76)(2, 18.432)The y-intercept is the y-value when x = 0.
Therefore, as the y-intercept is 1.8, a = 1.8.
[tex]\implies y=1.8b^x[/tex]
Substitute point (1, 5.76) into the equation and solve for b:
[tex]\begin{aligned} y&=1.8b^x\\\implies 5.76&=1.8 \cdot b^1\\5.76&=1.8b\\b&=\dfrac{5.76}{1.8}\\b&=3.2\end{aligned}[/tex]
Therefore, the exponential equation is:
[tex]\boxed{y=1.8(3.2)^x}[/tex]
To complete the given table, simply substitute the values of x into the found equation:
[tex]\begin{array}{c|l}x&\phantom{189}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{18}1.8\\\vphantom{\dfrac12}}1&\phantom{18}5.76\\\vphantom{\dfrac12}}2&\phantom{1}18.432\\\vphantom{\dfrac12}}3&\phantom{1}58.9824\\\vphantom{\dfrac12}}4&188.74368\end{array}[/tex]
Part (b)Given ordered pairs:
(0, 5)(2, 245)The y-intercept is the y-value when x = 0.
Therefore, as the y-intercept is 5, a = 5.
[tex]\implies y=5b^x[/tex]
Substitute point (2, 245) into the equation and solve for b:
[tex]\begin{aligned} y&=5b^x\\\implies 245&=5 \cdot b^2\\49&=b^2\\b&=\sqrt{49}\\b&=7\end{aligned}[/tex]
Therefore, the exponential equation is:
[tex]\boxed{y=5(7)^x}[/tex]
To complete the given table, simply substitute the values of x into the found equation:
[tex]\begin{array}{c|l}x&\phantom{11}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{1111}5\\\vphantom{\dfrac12}}1&\phantom{111}35\\\vphantom{\dfrac12}}2&\phantom{11}245\\\vphantom{\dfrac12}}3&\phantom{1}1715\\\vphantom{\dfrac12}}4&12005\end{array}[/tex]
Given h of x equals x squared minus 2 x minus 35, which statement is true?
The zeros of the quadratic equation: h(x) = x^2 - 2x - 35
are -5 and 7, thus the correct option is B.
What are the true statements?Here we have the quadratic equation:
h(x) = x^2 - 2x - 35
Using the quadratic formula we will get the two solutions:
[tex]x = \frac{2 \pm \sqrt{(-2)^2 - 4*1*-35} }{2*1} \\\\x = \frac{2 \pm 12 }{2} \\\\[/tex]
The solutions are:
x = (2 + 12)/2 = 7
x = (2 - 12)/2 = -5
Then the factors of the quadratic are (x - 7) and (x + 5), the correct option is B.
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(Area of Circles MC) A circular cookie cake costs $15.70. If the diameter of the cookie cake is 10 inches, what is the cost of one square inch of the cookie cake? Use π = 3.14.
The cost of one square inch of the cookie cake is $5.
What is area of circle?
The area encircled by a circle with radius r is known as πr^2 in geometry. Here, the Greek letter π stands for the constant proportion of a circle's circumference to its diameter, which is roughly equal to 3.14159.
Given:
A circular cookie cake costs $15.70.
The diameter of the cookie cake is 10 inches.
We have to find the cost of one square inch of the cookie cake.
Let the diameter is 10 inches.
So, the radius is 10/2 = 5 inches.
Area of circle = πr^2
= 3.14 x (5)^2
= 3.14 x 25
Area of circle = 78.5 square inches.
So, the cost of one square inch cookie cake is,
78.5 / 15.70 = 5
Hence, the cost of one square inch of the cookie cake is $5.
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Answer: The answer is $0.20.
Step-by-step explanation: Hope this helps! :)
what is the reciprocal of 8?
Answer:1/8
Step-by-step explanation:
The reciprocal of a number is what you multiply by a number to give 1. Therefore
8x = 1
x = 1/8
two more than a certian number is 15 less than the product of 7/8 and the number
The number is -136.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Let the number be x.
Given that, two more than the number, x, is 15 less than the product of 7/8 and the number, therefore:
x + 2 = (7/8)x - 15
x - (7/8)x = -15 -2
x/8 = -17
x = -136
Hence, the number is -136.
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Anna works at an electronics
store as a salesperson. Anna earns a 5% commission a
the total dollar amount of all
phone sales she makes, and earns a 7% commission Or
all computer sales. Anna made a total of $2100 in sales
and earned $119 in
commission. Write a system of equations that could be used to determine the dollar
amount of phone sales Anna made and the dollar amount of computer sales she
made. Define the variables that you use to write the system.
Let
Let p be the amount of sales (in dollars) of phones.
Let c be the amount of sales (in dollars) of computers.
Equation 1: sales
p + c = 2100
the amount of all sales is 2100
Equation 2: commission
0.05p + 0.07c = 119
5% commission on phones plus 7% commission on computers totals to 119
y=-3x-17 y=x-1 solving linear equations by substitions
x=-4, y=-5
You can substitute equation 2 into equation 1 since it's easier. After that, just substitute x=-4 back into equation 2.
78900 grams into kilograms
78.9 kg.
To convert 78,900 grams to kilograms, we can divide the number of grams by 1,000. Since 1 kilogram is equal to 1,000 grams, dividing the number of grams by 1,000 will give us the equivalent number of kilograms.
Therefore, 78,900 grams is equivalent to 78,900 / 1,000 = 78.9 kilograms.
You purchased 5,000 shares of a mutual fund at a price of $7.50 per share. You later sell those shares for $8.35 per share. During the time you owned the shares, the fund paid a dividend of $0.41 per share. Determine your investment return on the fund? Round answer to nearest tenth of a percent. Show your work
The required investment return on the fund is $6300 which is 16.8% of the investment.
Given that,
purchased 5,000 shares of a mutual fund at a price of $7.50 per share. Later sell those shares for $8.35 per share. During the time you owned the shares, the fund paid a dividend of $0.41 per share.
When someone applies for their money on something so that he can get a higher value in returns of his money.
Here,
Profit = 5000[8.35 + 0.41-7.50]
profit = $6300
Profit percentage = 6300 / [7.5 × 5000] × 100%
Profit percentage = 16.8%
Thus, the required investment return on the fund is $6300 which is 16.8% of the investment.
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Michael and Imani go out to eat for lunch.
Part A
If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer to the nearest cent.
Part B
After adding a tip, the total lunch cost was $32.24. What percentage tip did they give? Enter your answer to the nearest percentage.
Answer:
Part A: The bill is $27.32
Part B: The percentage is 19%
My work:
Part A
? 8
--------- = ---------
25.30 100
equals 2.02400
then round to get the tax amount which is $2.02
to find the bill cost we need to add the tax and the cost of the meal:
2.02 + 25.30 = 27.32
Part B
to find the tip we need to subtract the bill from the total lunch cost:
27.32 + t = 4.92 (t = tip)
32.24 - 27.32 = 4.92
So now that we know the tip we can figure out how much percentage that is of the cost of the meal:
4.92 ?
-------- = --------
25.30 100
which equals 19.4466403/100
the percentage is 19%
Sarah spent 30 minutes practicing her spelling words. She spent 3 times as much time reading. How many minutes did Sarah spend reading?
Sarah spends reading 30 min + [tex]0.05 min^{2}[/tex].
What is a mathematical expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.
However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.
The problem is in a mathematical expression.
30 min+3s min did Sarah spend reading
Convert s to min
.30min+3s min× 1min/60s
Cancel the common units and simplify.
Cross-cancel units.
30 min + [tex]0.05 min^{2}[/tex]
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Daniel rollerbladed 3 1/4 miles in 4 minutes. What was his speed in miles per hour?
Answer: 48 3/4 miles/hour.
Step-by-step explanation: To find Daniel's speed in miles per hour, we need to first convert the time he rollerbladed to hours. We can do this by dividing the number of minutes he rollerbladed by 60 minutes per hour, as follows:
time in hours = 4 minutes / 60 minutes/hour = 1/15 hours
We can then use the formula for speed, which is distance divided by time, to find Daniel's speed in miles per hour as follows:
speed in miles per hour = distance in miles / time in hours
speed in miles per hour = 3 1/4 miles / 1/15 hours
speed in miles per hour = 3 1/4 miles * 15 hours/1
speed in miles per hour = 48 3/4 miles/hour
Therefore, Daniel's speed in miles per hour was 48 3/4 miles/hour.
Answer:
Check explanation!
Step-by-step explanation:
Daniel rollerbladed at 15 mph, we know this because 60 divided by 4 = 15 (number of minutes in an hour divided by his time = answer)
so daniel rollerbladed at 15 mph
3,000 divided by 48 x 4
Answer:500 I hope this helpful
Step-by-step explanation:
3000 divided by 48 times 8
To make the calculation easier, first multiply the numbers that result in multiples of 10
24000 divided by 48
Divide the numbers
=500
Answer:
250
Step-by-step explanation:
If we follow the rules of PEMDAS, we go from left to right. Therefore, first, do 3,000 divided by 48.
3,000/48=62.5
Now, multiply 62.5 by 4.
62.5x4= 250
250 is your answer :D
Hope this helps and have a wonderful day!
"2. Compare and contrast the two major sects of Islam, Sunni and Shia, by filling out the table below. (10 points)
Similarities in the sects Differences between the sects"
The similarity is that Sunni and Shia Muslims agree on the fundamental tenets of Islam, such as worshiping Allah as God, acknowledging Muhammad (Peace Be Upon Him) as the Prophet, and adhering to the Quran's teachings.
The difference is that Shia place a greater emphasis on Muhammad's family ancestry through a succession of Imams than Sunnis do on imitating the Prophet and his example.
What is the Similarities and difference between the difference Islamic sect?All Shia and Sunni Muslims recognize the importance of the Quran; contrary to popular belief, Shi'a does not use a corrupted version of the Quran.
Shi'a and Sunni Muslims both use the Hadith, though they often prefer different collections of sayings.
They have different perspectives on imams. Imams are considered saints in Sunni Islam and must have a strong commitment to the Quran and Sunnah in order to be nominated. In Shia Islam, however, only God has the authority to name an imam. Only imams in Shia Islam have the authority to translate the Quran.
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Susan runs 6 miles in 50 minutes. At the same rate, how many miles would she run in 35 minutes?
Answer:
Step-by-step explanation:
4.2 miles
PLEASE HELP IM SCREWED
Number 13 and 15
Answer:7
Step-by-step explanation:
Solve the following equations
25x²-4=0
Answer: x= (2)/5 & x= (-2)/5
Step-by-step explanation:
Factor Form:
1. Use the sum product patturn
25x^2-4=0 → 25x^2+10-10-4=0
2. Common factors from each pair
25x^2+10-10-4=0 → 5x(5x+2)-2(5x+2)=0
3. Rewrite the factored form
5x(5x+2)-2(5x+2)=0 → (5x+2)(5x-2)=0
4. Create separate equations
(5x+2)(5x-2)=0 → 5x+2=0 5x-2=0
5. Solve
5x+2=0 5x-2=0 → x=(2)/5 x=(-2)/5
Four students in Mr. Morales' math classes are
conducting surveys in their school. They each
handed out 100 surveys. The table shows the
response rates of each student's survey.
Response Rates
Min-seo: 4 out of 5 students responded
Orlando: 8 out of 10 students responded
Jian: 3 out of 4 students responded
Leona: 10 out of 12 students responded
2. Did Min-seo and Orlando get the same ratio of responses? Explain.
3. Did Jian and Leona get the same ratio of responses? Explain.
Min-Seo and Orlando have the same ratio of responses but Jian and Leona do have not the same ratio of responses.
What is ratio?The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.
As per the given information in the question,
The ratios given in the question are,
2.
The ratio obtained by Min-SEO = 4/5 and,
The ratio obtained by Orlando = 8/10
The ratio in the simplest form will be: 4/5
This means that Nin-SEO and Orlando have the same ratio of responses.
3.
The ratio obtained by Jian = 3/4 and,
The ratio obtained by Leona = 10/12
The simplest form of ratio = 5/6
This means that Jian and Leona do have not the same ratio of responses.
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A contractor has 18 gallons of paint that will cover 2,808 square feet
The rate that best represents the relationship between the number of square feet and the number of gallons of paint is 156 square feet per gallon of paint.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that a contractor has 18 gallons of paint that will cover 2,808 square feet. Therefore, the relationship between the number of square feet and the number of gallons of paint can be written as,
Number of square feet per gallon of paint
= Total area painted by 18 gallons / Total area of the paint
= 2,808 square feet / 18 gallons
= 156 square feet per gallon of paint
Hence, the correct option is C.
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The complete question is:
A contractor has 18 gallons of paint which will cover 2,808 square feet. Which of the following rates best represents the relationship between the number of square feet and the number of gallons of paint?
1 point
A. 182 gallons of paint per square foot
B. 2,912 gallons of paint per square foot
C. 156 square feet per gallon of paint
D. 16 square feet per gallon of paint
I need the answer for this
Answer: 3.46
Step-by-step explanation:
5[tex]u^{2}[/tex] = 60
[tex]u^{2}[/tex] = 12
u = [tex]\sqrt{12}[/tex]
u = 3.46
Mrs. Williams assigned her class a project to find the height of a flagpole. The students could not measure the height, so they used a mirror to determine the height of the flagpole. Jerrica placed a mirror on the ground 20 feet from the base of the flagpole and backed up until the top of the pole was centered in the mirror. Jerrica is 5.6 feet tall and is standing 7.4 feet from the mirror.
What is the height of the flagpole?
With the help of similar triangles the height of Flagpole is 15.13 feet
what is similar triangle?
Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.
solution:
let C is the point of reflection in triangle ABC and EDC
∠ ABC = ∠ EDC ( 90 Degree)
∠ ACD = ∠ ECD ( Reflective angle )
By symmetry,
AB/ED = BC/CD
5.6/ x = 7.4 / 20
x = 15.13 feet
Hence the height of flagpole is 15.13 feet
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Please help! The answer is the slope and it needs to be rounded to 3 decimal places.
The slope is 0.003
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
the coordinates are (12000, 20) and (18000, 2)
so, slope= 18 / 6000
= 0.003
The 3 in the thousandths place rounds down to 3, or stays the same, because the digit to the right in the ten thousandths place is 0.003.
Hence, the slope is 0.003.
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Determine the values of A, B, and C when y- 7= 3(x-4) is written in standard form, Ax+By = C.
Answer:
A = 3
B = -1
C = 5
Step-by-step explanation:
y - 7 = 3(x - 4) Distribute the 3
y - 7 = 3x -12 subtract y from both sides
-7 = 3x -y -12 Add 12 to both sides
5 =3x -y Flip the equation around the equal sign
3x -y = 5
The 3 is the A, -1 is the B and 5 is the C.
x/7= -10 what is the answer????
The answer is x = -70.
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
Multiply all terms by the same value to eliminate fraction denominators
/7 = −10
7⋅/7 = 7(−10)
Cancel multiplied terms that are in the denominator
7⋅/7 = 7 (−10)
x =7(-10)
Multiply the numbers
=7(−10)
=−70.
Hence The answer is x = -70.
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4. Which of the triangles below is not a right triangle?
3 cm, 4 cm, 5 cm
27 cm, 36 cm, 45 cm
6 ft, 8 ft, 12 ft
√6in, √10in, √4in
Answer:
3cm,4cm,5cm
Step-by-step explanation:
5 is the longest side ( the hypotenuse)
and by Pythagoras theorem x=√(3²+4²)
= √(9+16)
=√(25)
= 5
so 3cm,4cm,5cm is a right angle triangle.
x=√(27²+36²)
=√(729+ 1296)
=√2025
=45
so 27cm,36cm,45cm is a right angle triangle
to find out if a triangle is a right angle triangle try applying the law of Pythagoras theorem to see if it matches, and if it matches then it is a right angle triangle but if it doesn't then it's not a right angled triangle Try for the last two and put it down the comments I'll try to checkwhich figure should be next, following the pattern?
The figure that should be the next, following the pattern is option (b)
How to determine the next figure?The missing information that completes this question is added as an attachment
From the attached figure, we have the following pattern:
Each of the figure represents the alphabet letter PThe next figure is gotten by rotating the current figure by 45 degrees to the right i.e. in clockwise directionWhen the pattern is studied carefully, we can see that the next figure is the figure in option (b)
This is so because the figure in option (b) is gotten by rotating the last figure in the pattern by 45 degrees to the right
Hence, the conclusion about the figure that should be the next figure is that the next figure should be figure (b)
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For what value of x is line m parallel to line n?
Answer: x=-2
Step-by-step explanation:
they’re corresponding angles meaning they’re congruent or equal to each other then solve like any other problem
What is Four divided by 1 8. It’s a faction the one and eight
Answer: 32
Step-by-step explanation:
4 ÷ 1/8
You can reduce the expression by cancelling out common factors;
4/1 ÷ 1/8
Cross cancel the ones, and then multiply 4 and 8
4 x 8 = 32